Question
You have just been hired at ABC Inc. on January 1st 2018. On your first day of work, you notice that ABC Inc. owns $1
You have just been hired at ABC Inc. on January 1st 2018. On your first day of work, you notice that ABC Inc. owns $1 million in bonds that earn a floating rate of interest of LIBOR + 0.5% with maturity in 3 years on January 1st 2021. ABC Inc. also has an existing debt of $1 million on which it pays a fixed rate of interest of 4% with maturity in 3 years on January 1st 2021. You identify that there is an opportunity to hedge the companys interest rate risk. You offer your manager to enter into an interest rate swap to transform the $1 million existing debt of ABC Inc. The swap has a maturity of 3 years, maturing on January 1st, 2021. Payments are exchanged once on January 1st of each year. The fixed-rate leg of the swap has an interest rate of 4% (annual rate with annual compounding) and the floating-rate leg of the swap has an interest rate equivalent to the 1-year LIBOR + 0.75%. On January 1st 2019, the zero-coupon 1-year LIBOR rate was 4.5% (annual rate with continuous compounding). On July 1st 2019, the zero-coupon 6-month, 1-year, 1.5-year, and 2-year LIBOR rates are 4.7%, 4.9%, 5.3%, and 5.7% respectively (annual rates with continuous compounding). The annual forward rate for a loan starting in 6 months and ending in 1.5 years is 4.8% (annual rate with continuous compounding). On July 1st, 2019, your manager wants to know the value of the swap. Assume the OIS and the LIBOR rates are the same. Round all your calculations to 5 decimal places. Round your final answer to 2 decimal places.
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